Hong Life CalculatorsUnderstanding the radiation pressure calculator — concept and principle
This calculator finds the pressure light exerts on a surface from its intensity and the surface's reflectance, and the resulting force, acceleration and speed gained per day for a given area and mass. It is used for solar-sail examples, spacecraft orbit perturbations and physics courses.
How it is calculated
p = (1 + R) × I ÷ c
Absorber: p = I ÷ c; perfect mirror: p = 2I ÷ c
Force F = p × A; acceleration a = F ÷ m; speed per day = a × 86,400 s
- I in W/m², R the reflectance (0–1), c = 299,792,458 m/s; 1 Pa = 1 N/m².
The principle
Light carries momentum as well as energy: a beam of power P carries momentum P/c per second. When it is absorbed, that momentum is transferred to the surface; when it is reflected, the light's momentum reverses, so the surface receives twice as much. The pressure is tiny because c is so large, but in space there is no friction, so even a tiny steady push builds up speed over days and months.
Worked example
Default inputs: I = 1,370 W/m² (sunlight near Earth), R = 100%, A = 32 m², m = 5 kg.
- p = 2 × 1,370 ÷ 299,792,458 = 9.14 µPa (0.00000914 Pa).
- F = 9.14 × 10⁻⁶ × 32 = 0.0002925 N.
- a = 0.0002925 ÷ 5 = 0.00005849 m/s².
- Speed gained per day = 0.00005849 × 86,400 = 5.054 m/s.
- A perfect absorber would feel half: 4.57 µPa.
How to read the result
Sunlight at Earth's distance pushes with only a few micropascals, about one ten-billionth of atmospheric pressure. Yet a light solar sail gains several metres per second each day, which over months is useful propulsion. The pressure falls with the square of distance from the Sun.
Common mistakes
- Forgetting the factor of 2 for reflection.
- Ignoring the angle: light hitting at an angle pushes less.
- Expecting noticeable effects on Earth, where gravity and air dominate.
Frequently asked questions
How strong is sunlight's pressure on Earth?
About 4.6 µPa on an absorber and 9.1 µPa on a mirror.
Why does reflection double the pressure?
The light's momentum is reversed, so twice the momentum is transferred.
Can radiation pressure move spacecraft?
Yes; solar-sail missions have demonstrated it.
Does it affect satellites?
Yes, it slightly perturbs orbits and must be included in precise tracking.
Sources: OpenStax, University Physics Volume 2 (2016), section 16.4 "Momentum and Radiation Pressure"